Problem 2. Two identical mass m fermions are in the same spin state ("up"), and they are moving in a one-dimensional harmonic oscillator potential of frequency w. Show that the time-independent Schroedinger equation can be separated in BOTH the separate particle (x1,le coordinate system AND in the relative and centerofmass coordinate system. (a) Give the two energy level formulas of this identical two-fermion system in terms of quantum numbers appropriate to each case; these will involve different quantum numbers associated with the two different coordinate systems. (b) Compute the degeneracies of the first four different energy levels of this spin-polarized fermionic system and show that they are the same for both coordinate systems used in your solution to part (a)